1. Field of the Invention
The present invention relates to an approximation method for signal-to-noise ratio soft information for a transmitter of a communications system, and more particularly, to an approximation method for approximating signal-to-noise ratio soft information with a probability distribution model.
2. Description of the Prior Art
To achieve expected communication functions and quality in a wireless communications system, different modulation and coding schemes (MCS), having different modulation techniques, coding rates, etc. for different data rates, are defined in associated specifications, with each different modulation and coding scheme distinguished by an index. For example, in a wireless communications system complying with IEEE 802.11n standard, MCS-15 represents a modulation and coding scheme using 64-QAM and a coding rate of 5/6, and relates to data rates of 20 MHz or 40 MHz according to the selected bandwidth. The communications system can select an appropriate MCS from current modulation and coding schemes, for achieving the expected throughput.
In the wireless communications system, a transmission channel is not ideal, and transmission failure occurs due to many factors, such as multipath transmission, noise, and interference caused by electronic equipment. When the environment of the transmission channel changes, a transmitter of the wireless communications system may have to reselect the modulation and coding scheme for a higher data rate when the channel condition is good, or for a lower data rate when the channel condition is getting worse, so that the throughput of the wireless communications system can be maintained at an acceptable level.
When the transmitter has no idea about the channel condition, the transmitter can only estimate the channel condition through transmission results of transmitted packets, i.e. positive acknowledgements (ACKs) or negative acknowledgements (NACKs), transmitted by a receiver of the communications system. In order to determine the channel condition, several methods are adapted, including an Auto Rate Fallback (ARF) algorithm, an adaptive ARF (AARF) algorithm, a sample rate algorithm, an Onoe algorithm, an adaptive Multi Rate Retry (AMRR) algorithm, a Multiband Atheros Driver for WiFi (Madwifi) algorithm, and a Robust Rate Adaptation algorithm (RRAA). The ARF and AARF algorithms use probe packets to determine whether a data rate higher than the current one can be achieved, and decreases the data rate when consecutive transmission failures occur. The sample rate algorithm periodically transmits probe packets with randomly-selected modulation and coding schemes, and uses the modulation and coding scheme that achieves the highest throughput for transmitting normal data packets. The Onoe algorithm uses a specific data rate to transmit packets for a period of time, and increases the data rate to a higher level when the packet error rate in the period is lower than 10%. The AMRR and Madwifi algorithms use probe packets and two packet correct rate thresholds to determine whether to step up or step down the data rate. The RRAA algorithm determines the data rate according to the received ACK and the packet correct rate.
In summary, in most conventional rate adaptation methods, the method determines whether to update the data rate by transmitting additional probe packets or by estimating the transmission quality for a period of time. For the application service of real time communications, the above rate adaptation methods take a great deal of time to update the data rate and cannot improve the throughput efficiently. Therefore, in Taiwan patent application No. 97146118, the Applicant discloses a rate adaptation method in which a transmitter of the wireless communications system updates a conditional probability density function (PDF) of signal-to-noise ratio (SNR) according to a conditional PDF of receiving a response message of a latest transmitted packet and a conditional PDF of SNR corresponding to a packet immediately preceding the latest transmitted packet, and the transmitter reselects a proper modulation and coding scheme for a next packet to be transmitted. Note that the conditional PDF of SNR is called SNR soft information.
Note that the conditional PDF of SNR mentioned in Taiwan patent application No. 97146118 is the conditional PDF of SNR given received signal strength indication (RSSI) values and the ACK/NACK of all transmitted packets with various modulation and coding schemes, denoted by p(SNR|RSSI, MCSs, ACKs/NACKs). The conditional PDF of SNR is updated every time an ACK or a NACK is received. The conditional PDF of SNR is given by:
                                          p            ⁡                          (                                                                    S                    ⁢                                                                                  ⁢                    N                    ⁢                                                                                  ⁢                    R                                    |                                      R                    ⁢                                                                                  ⁢                    S                    ⁢                                                                                  ⁢                    S                    ⁢                                                                                  ⁢                    I                                                  ,                MCSs                ,                                  ACKs                  /                  NACKs                                            )                                =                                    p              ⁡                              (                                                      S                    ⁢                                                                                  ⁢                    N                    ⁢                                                                                  ⁢                    R                                    |                                      R                    ⁢                                                                                  ⁢                    S                    ⁢                                                                                  ⁢                    S                    ⁢                                                                                  ⁢                    I                                                  )                                      ⁢                                          ∏                                  i                  =                  0                                N                            ⁢                                                          ⁢                                                p                  ⁡                                      (                                                                                            ACKi                          /                          NACKi                                                |                                                  S                          ⁢                                                                                                          ⁢                          N                          ⁢                                                                                                          ⁢                          R                                                                    ,                      MCSi                                        )                                                                    p                  ⁡                                      (                                                                  ACKi                        /                        NACKi                                            |                      MCSi                                        )                                                                                      ,                            (        1        )            
where N is the number of accumulated transmitted packets, MCSi is the modulation and coding scheme used for an ith transmitted packet, and ACKi/NACKi indicates a response message, which can be an ACK or a NACK, of the ith transmitted packet. Note that the transmitter not receiving an ACK in time is also regarded as receiving a NACK. p(SNR|RSSI) is the conditional PDF of SNR given various RSSI values before any ACK/NACK is received. p(ACKi/NACKi|MCSi) is the probability of receiving an ACK/NACK of the ith transmitted packet given the modulation and coding scheme MCSi. p(ACKi/NACKi|SNR, MCSi) is a conditional PDF of receiving an ACK/NACK of the ith transmitted packet given MCSi with various SNRs. The equation (1) can be further represented as:
                                                        p              ⁡                              (                                                                            S                      ⁢                                                                                          ⁢                      N                      ⁢                                                                                          ⁢                      R                                        |                                          R                      ⁢                                                                                          ⁢                      S                      ⁢                                                                                          ⁢                      S                      ⁢                                                                                          ⁢                      I                                                        ,                  MCSs                  ,                                      ACKs                    /                    NACKs                                                  )                                      N                    =                                                    p                ⁡                                  (                                                                                    S                        ⁢                                                                                                  ⁢                        N                        ⁢                                                                                                  ⁢                        R                                            |                                              R                        ⁢                                                                                                  ⁢                        S                        ⁢                                                                                                  ⁢                        S                        ⁢                                                                                                  ⁢                        I                                                              ,                    MCSs                    ,                                          ACKs                      /                      NACKs                                                        )                                                            N                -                1                                      ×                                          p                ⁡                                  (                                                                                    ACK                        N                                            |                                              S                        ⁢                                                                                                  ⁢                        N                        ⁢                                                                                                  ⁢                        R                                                              ,                                          MCS                      N                                                        )                                                            p                ⁡                                  (                                                            ACK                      N                                        |                                          MCS                      N                                                        )                                                                    ,                  and          ⁢                                          ⁢                                    p              ⁡                              (                                                                            S                      ⁢                                                                                          ⁢                      N                      ⁢                                                                                          ⁢                      R                                        |                                          R                      ⁢                                                                                          ⁢                      S                      ⁢                                                                                          ⁢                      S                      ⁢                                                                                          ⁢                      I                                                        ,                  MCSs                  ,                  ACKs                  ,                  NACKs                                )                                      N                                              (        2        )                                                      p            ⁡                          (                                                                    S                    ⁢                                                                                  ⁢                    N                    ⁢                                                                                  ⁢                    R                                    |                                      R                    ⁢                                                                                  ⁢                    S                    ⁢                                                                                  ⁢                    S                    ⁢                                                                                  ⁢                    I                                                  ,                MCSs                ,                                  ACKs                  /                  NACKs                                            )                                            N            -            1                          ×                                            1              -                              p                ⁡                                  (                                                                                    ACK                        N                                            |                                              S                        ⁢                                                                                                  ⁢                        N                        ⁢                                                                                                  ⁢                        R                                                              ,                                          MCS                      N                                                        )                                                                    1              -                              p                ⁡                                  (                                                            ACK                      N                                        |                                          MCS                      N                                                        )                                                              .                                    (        3        )            
The equation (2) shows the conditional PDF of SNR when the response message is an ACK, and the equation (3) shows the conditional PDF of SNR when the response message is a NACK. In other words, when the transmitter receives the response message of the Nth packet, the transmitter obtains the conditional PDF of SNR corresponding to the Nth packet, p(SNR|RSSI, MCSs, ACKs/NACKs)N, according to the conditional PDF of SNR corresponding to an (N−1)th packet, p(SNR|RSSI, MCSs, ACKs/NACKs)N−1, and the conditional PDF of receiving the response message of the Nth packet with various SNRs, p(ACKN|SNR, MCSN) or 1−p(ACKN|SNR, MCSN).
In addition, after the conditional PDF of SNR corresponding to the (N−1)th packet is obtained, the transmitter selects a modulation and coding scheme MCSN for the Nth packet according to the conditional PDF of SNR corresponding to the (N−1)th packet. Next, after the response message of the (N+1)th packet is received, the transmitter obtains a conditional PDF of SNR corresponding to the Nth packet and selects a modulation and coding scheme MCSN+1 for the (N+1)th packet accordingly. Note that selection of the modulation and coding scheme is disclosed in Taiwan patent application No. 97146118 and detailed description thereof is not given here. Briefly, the modulation and coding scheme is reselected every time a response message is received in the rate adaptation method disclosed in Taiwan patent application No. 97146118. Therefore, the transmitter can find the optimized data rate with an acceptable throughput as soon as possible.
From the above equations (1), (2) and (3), the transmitter performs the multiplication of p(SNR|RSSI, MCSs, ACKs/NACKs)N−1 and p(ACKN|SNR, MCSN) for updating the conditional PDF of SNR. In other words, the transmitter has to perform the multiplication for each SNR value. Please refer to FIG. 1, which is a diagram of the conditional PDF of receiving an ACK given the modulation and coding scheme versus various SNRs for a conventional transmitter of a wireless communications system complying with IEEE 802.11n standard. As in FIG. 1, the range of SNR is from 0 dB to 30 dB. If the sampling interval of SNR is 0.1 dB, for example, the transmitter has to perform hundreds of multiplications of conditional PDFs to obtain the conditional PDF of SNR. In this situation, the operation complexity is quite high, and the efficiency of the transmitter is reduced.